Stanley, Richard P. A bound on the spectral radius of graphs with \(e\) edges. (English) Zbl 0617.05045 Linear Algebra Appl. 87, 267-269 (1987). Author’s abstract: ”The spectral radius \(\rho(A)\) of the adjacency matrix \(A\) of a graph \(G\) with \(e\) edges satisfies \(\rho(A)\leq (- 1+\sqrt{1+8e})/2\). Equality occurs if and only if \(e=\binom{k}{2}\) and \(G\) is a disjoint union of the complete graph \(K_k\) and isolated vertices.” Reviewer: Dragoš Cvetković (Beograd) Cited in 2 ReviewsCited in 74 Documents MSC: 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) Keywords:spectral radius; adjacency matrix PDFBibTeX XMLCite \textit{R. P. Stanley}, Linear Algebra Appl. 87, 267--269 (1987; Zbl 0617.05045) Full Text: DOI References: [1] Brualdi, R. A.; Hoffman, A. J., On the spectral radius of (0,1)-matrices, Linear Algebra Appl., 65, 133-146 (1985) · Zbl 0563.15012 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.